A bookstore has 15 copies of a particular textbook, of which 6 are first printings and the other 9 are second printings. Suppose that 5 of these copies are randomly selected, and let X be the number of first printings among the selected copies.

a) What kind of a distribution does X have? (name and values of parameters)
b) Computer P(X=2), P( X<=2), P(X>=2)
c) Calculate the mean and standard deviation of X.

a) For this case the random variable X follows a hypergometric distribution.

With parameters N=15, M=6 n =5

Where N=15 is the population size, M=6 is the number of success states in the population, n=5 is the number of draws, k is the number of observed successes  

b)

We can find the individual probabilities:

And we got:

c)

And the deviation would be the square root of the variance:

Step-by-step explanation:

Previous concepts

The hypergeometric distribution is a discrete probability distribution that its useful when we have more than two distinguishable groups in a sample and the probability mass function is given by:

Where N=15 is the population size, M=6 is the number of success states in the population, n=5 is the number of draws, k is the number of observed successes  

The expected value and variance for this distribution are given by:

a) What kind of a distribution does X have? (name and values of parameters)

For this case the random variable X follows a hypergometric distribution.

With parameters N=15, M=6 n =5

b) Computer P(X=2), P( X<=2), P(X>=2)

Using the pmf we have this:

For

We can find the individual probabilities:

And we got:

For the last case we can do this using the complement rule

Part c

The expected value and variance for this distribution are given by:

And the deviation would be the square root of the variance: